Many retirees in the U. S. have portfolios that have largely been accumulated on a tax deferred basis. Tax will have to be paid, however, on any funds disbursed from the portfolio. Moreover, Required Minimum Distributions (RMD) may make taxable disbursements necessary in excess of those needed to cover living expenses and pay tax on those disbursements. Suppose initially that the entire portfolio has been accumulated on a tax deferred basis. No tax is payable on any income received on investments in the portfolio, or on transactions made within the portfolio. Any disbursements made from the portfolio, however, must be added to taxable income.
To consider the effect of the tax for a specific case suppose without the tax that an individual would make a 4.0% initial disbursement under the conditions considered at page, BID, in Charts 5.13 and 5.l4. Now suppose instead of being tax free that the portfolio is a tax deferred portfolio as just described. Suppose also that the individual has just turned 65 and is subject to the tax brackets and rules in 2023, and that these brackets and rules will continue in the future. The individual also has other taxable income and is using the standard deduction. Each year, tax will have to be paid on the disbursement from the portfolio plus $10,000 in real terms. Determining the tax that will have to be paid each year requires extensive changes to the model, which are described in a note.
Suppose that the individual continues to disburse 4.0% from the portfolio initially to cover living expenses, but now has to also make additional disbursements to cover the taxes. If the initial value of the portfolio is $1 million the effect of the tax payments on the sustainability of the disbursements to cover living expenses is shown by the dashed curves in Charts 10.1 and 10.2. The solid curves in these charts show the disbursement without the tax, and are the same as for the 4.0% initial disbursement without the tax in Charts 5.13 and 5.14 at page BID.
The dashed curves show that the taxes on a $1 million portfolio cause a moderate reduction in sustainability at year 12, and a serious reduction at year 24. To get the same chances of a decline at year 24 as without the tax, Chart 10.3 shows that the initial disbursement must be reduced from 4.0% to 3.6%. For a $4 million portfolio Chart 10.4 shows that a further reduction is required in the initial disbursement from 3.6% to 3.4%. With the tax, beneficiaries will have to decide how much of a reduction in the initial disbursement is warranted to improve sustainability.
An interesting question is the extent to which these results are being affected by the Required Minimum Distribution (RMD) requirements. As these requirements do not begin until age 73, they might account for the much more serious effect of the tax at year 24 than at year 12. As discussed in the note, the analysis assumes that any funds withdrawn due to the RMD that are not needed to cover living expenses or pay taxes are invested in a reserve that earns a zero after tax real return. This reserve is available to cover withdrawals when they exceed the RMD, or to provide funds if the tax deferred portfolio is exhausted. The size of the reserve at any time is available as an output of the simulations, and indicates the importance of the RMD in affecting the tax that is being paid.
The size of this reserve at years 12, 24, and 36 is shown in Chart 10.5 when 4.0% is disbursed initially. The chart shows that there is almost a .70 chance that there is nothing in the reserve at the back of the period. Thus, the RMD have little effect on the tax that is paid. When the initial disbursement is reduced from 4.0% to 3.6%, however, there is a somewhat larger accumulation of funds in the portfolio. In this case, about half instead of a third of the time the RMD causes the payment of additional tax. There is some chance that the RMD will cause large increases in the tax, but these chances are very small. Note also that there is very little chance that there will be any funds in the reserve at year 12, which corresponds to age 76. Thus, the recent increase in the age at which the RMD becomes effective from age 72 to 73 had little effect on the tax that has to be paid.
Conclusions
Many retirees in the U. S. have portfolios that have largely been accumulated on a tax deferred basis. No tax is payable on income or gain and loss. Any disbursements, however, must be added to taxable income. The implications of the tax have been investigated for a single taxpayer starting with a 4.0% disbursement at age 65, assuming the tax brackets and rules in 2023 apply. To avoid increased chances of a decline at year 24, the initial disbursement must be reduced from 4.0% to 3.6% for a $1 million, and 3.4% for a $4 million portfolio. The RMD are applicable less than half the time.
Note
At the beginning of t, let Tx(t), TxInc(t), RMD(t), and Rsv(t) denote respectively the tax paid, taxable income, the RMD, and the funds in the reserve. Tax is calculated in dollars from taxable income in dollars, whereas C(t) and V(t) in the model are expressed as a percentage of initial portfolio value. For the tax calculations, C(t) and V(t) must be multiplied by a factor, s, to express them in dollars, and Tx(t) must be divided by s to express the tax payment as a percentage of initial portfolio value when it is deducted from V(t) in the model. For an initial portfolio of $1 million s is 10,000 so that a disbursement of 4.0% becomes $40,000. For an initial portfolio of $4 million, s is equal to 40,000 so that a 4.0% disbursement becomes $160,000. The beneficiary is age 65 at year 1 and becomes age 73 at year 9. The RMD are assumed to start at the beginning of year 9 with the factor for a single filer at age 73 in the 2023 rules of 26.5. Thus, RMD(9) = s*V(9)/26.5 and subsequent RMD are given by the respective factors for later ages in the 2023 rules. TxInc(t) is calculated from the portfolio withdrawals at the beginning of t plus an assumed $10,000 in real terms each year to allow for taxable Social Security less the standard deduction for a single filer age 65 or older. Tx(t) is calculated from TxInc(t-1) based on a sum of conditional statements for each of the seven tax brackets in 2023. For example, the conditional statements for the first three brackets, which are the relevant range for a $1 million portfolio, are the following:
Prior to year 9 when the RMD begin the withdrawals from the portfolio to get taxable income are equal simply to s*C(t)+Tx(t). At year 10, however, determining the taxable withdrawal from the portfolio is more complicated because there may be funds in the reserve in the prior year that cover at least part of s*C(t)+Tx(t) if s*C(t)+Tx(t) is larger than RMD(t). At year 10 and thereafter the withdrawal from the portfolio is given by the relation in (1):
Moreover, Rsv(t-1) is included with V(t) in the calculation of the limit on C(t) given by C*(t). As a result, the withdrawal given by (1) could at some point exceed V(t). In such an event any funds in the portfolio are used to cover as much of the withdrawal as possible and the remainder is obtained from the reserve. Subsequent s*C(t)+Tx(t) are covered from the reserve.
Taking into account the possibility that V(t) may not be larger than the withdrawal given
by (1), V(t+1) is given by:
If(V(t) >(1),(V(t)–(1))*(1+R(t)),0)
and TxInc(t) by:
If(V(t)>(1),(1),V(t))+10,000
Since V(t+1)=0 when V(t)<=(1) note that RMD(t+1) is also zero in this case. Moreover, at t+1 (1) is also zero because (1) is equal to the RMD when the withdrawal is being funded by the reserve and RMD(t+1)=0. TxInc(t+1) is therefore equal to 10,000 in this case as are subsequent values of taxable income.
RMD(t) adds to the reserve when it exceeds s*C(t)+Tx(t). The reserve is reduced when RMD(t) is less than s*C(t)+Tx(t), and there are funds in the reserve. Assuming V(t)>(1) the change in the reserve at the beginning of t is therefore given by (2):
If V(t)<=(1), V(t) is deducted from the portfolio and the remainder of the withdrawal at t comes from the reserve. Any further withdrawals in the future come from the reserve. The value of Rsv(t) is therefore given by the following relation:
Taxes
Tax Deferred Portfolios
Many retirees in the U. S. have portfolios that have largely been accumulated on a tax deferred basis. Tax will have to be paid, however, on any funds disbursed from the portfolio. Moreover, Required Minimum Distributions (RMD) may make taxable disbursements necessary in excess of those needed to cover living expenses and pay tax on those disbursements. Suppose initially that the entire portfolio has been accumulated on a tax deferred basis. No tax is payable on any income received on investments in the portfolio, or on transactions made within the portfolio. Any disbursements made from the portfolio, however, must be added to taxable income.
To consider the effect of the tax for a specific case suppose without the tax that an individual would make a 4.0% initial disbursement under the conditions considered at page, BID, in Charts 5.13 and 5.l4. Now suppose instead of being tax free that the portfolio is a tax deferred portfolio as just described. Suppose also that the individual has just turned 65 and is subject to the tax brackets and rules in 2023, and that these brackets and rules will continue in the future. The individual also has other taxable income and is using the standard deduction. Each year, tax will have to be paid on the disbursement from the portfolio plus $10,000 in real terms. Determining the tax that will have to be paid each year requires extensive changes to the model, which are described in a note.
Suppose that the individual continues to disburse 4.0% from the portfolio initially to cover living expenses, but now has to also make additional disbursements to cover the taxes. If the initial value of the portfolio is $1 million the effect of the tax payments on the sustainability of the disbursements to cover living expenses is shown by the dashed curves in Charts 10.1 and 10.2. The solid curves in these charts show the disbursement without the tax, and are the same as for the 4.0% initial disbursement without the tax in Charts 5.13 and 5.14 at page BID.
The dashed curves show that the taxes on a $1 million portfolio cause a moderate reduction in sustainability at year 12, and a serious reduction at year 24. To get the same chances of a decline at year 24 as without the tax, Chart 10.3 shows that the initial disbursement must be reduced from 4.0% to 3.6%. For a $4 million portfolio Chart 10.4 shows that a further reduction is required in the initial disbursement from 3.6% to 3.4%. With the tax, beneficiaries will have to decide how much of a reduction in the initial disbursement is warranted to improve sustainability.
An interesting question is the extent to which these results are being affected by the Required Minimum Distribution (RMD) requirements. As these requirements do not begin until age 73, they might account for the much more serious effect of the tax at year 24 than at year 12. As discussed in the note, the analysis assumes that any funds withdrawn due to the RMD that are not needed to cover living expenses or pay taxes are invested in a reserve that earns a zero after tax real return. This reserve is available to cover withdrawals when they exceed the RMD, or to provide funds if the tax deferred portfolio is exhausted. The size of the reserve at any time is available as an output of the simulations, and indicates the importance of the RMD in affecting the tax that is being paid.
The size of this reserve at years 12, 24, and 36 is shown in Chart 10.5 when 4.0% is disbursed initially. The chart shows that there is almost a .70 chance that there is nothing in the reserve at the back of the period. Thus, the RMD have little effect on the tax that is paid. When the initial disbursement is reduced from 4.0% to 3.6%, however, there is a somewhat larger accumulation of funds in the portfolio. In this case, about half instead of a third of the time the RMD causes the payment of additional tax. There is some chance that the RMD will cause large increases in the tax, but these chances are very small. Note also that there is very little chance that there will be any funds in the reserve at year 12, which corresponds to age 76. Thus, the recent increase in the age at which the RMD becomes effective from age 72 to 73 had little effect on the tax that has to be paid.
Conclusions
Many retirees in the U. S. have portfolios that have largely been accumulated on a tax deferred basis. No tax is payable on income or gain and loss. Any disbursements, however, must be added to taxable income. The implications of the tax have been investigated for a single taxpayer starting with a 4.0% disbursement at age 65, assuming the tax brackets and rules in 2023 apply. To avoid increased chances of a decline at year 24, the initial disbursement must be reduced from 4.0% to 3.6% for a $1 million, and 3.4% for a $4 million portfolio. The RMD are applicable less than half the time.
Note
At the beginning of t, let Tx(t), TxInc(t), RMD(t), and Rsv(t) denote respectively the tax paid, taxable income, the RMD, and the funds in the reserve. Tax is calculated in dollars from taxable income in dollars, whereas C(t) and V(t) in the model are expressed as a percentage of initial portfolio value. For the tax calculations, C(t) and V(t) must be multiplied by a factor, s, to express them in dollars, and Tx(t) must be divided by s to express the tax payment as a percentage of initial portfolio value when it is deducted from V(t) in the model. For an initial portfolio of $1 million s is 10,000 so that a disbursement of 4.0% becomes $40,000. For an initial portfolio of $4 million, s is equal to 40,000 so that a 4.0% disbursement becomes $160,000. The beneficiary is age 65 at year 1 and becomes age 73 at year 9. The RMD are assumed to start at the beginning of year 9 with the factor for a single filer at age 73 in the 2023 rules of 26.5. Thus, RMD(9) = s*V(9)/26.5 and subsequent RMD are given by the respective factors for later ages in the 2023 rules. TxInc(t) is calculated from the portfolio withdrawals at the beginning of t plus an assumed $10,000 in real terms each year to allow for taxable Social Security less the standard deduction for a single filer age 65 or older. Tx(t) is calculated from TxInc(t-1) based on a sum of conditional statements for each of the seven tax brackets in 2023. For example, the conditional statements for the first three brackets, which are the relevant range for a $1 million portfolio, are the following:
If(And(TxInc(t-1) > 0,TxInc(t-1)<=11,000),.10*TxInc(t-1),0)+
If(And(TxInc(t-1)>11,000,TxInc(t-1)<= 44,725),1,100+.12*(TxInc(t-1)–11,000),0)+
If(And(TxInc(t-1)>44,725,TxInc(t-1)<=95,775),5,147+.22*(TxInc(t-1)–44,725),0)
Prior to year 9 when the RMD begin the withdrawals from the portfolio to get taxable income are equal simply to s*C(t)+Tx(t). At year 10, however, determining the taxable withdrawal from the portfolio is more complicated because there may be funds in the reserve in the prior year that cover at least part of s*C(t)+Tx(t) if s*C(t)+Tx(t) is larger than RMD(t). At year 10 and thereafter the withdrawal from the portfolio is given by the relation in (1):
(1) If(RMD/s>=C(t)+Tx(t)/s,RMD(t)/s,If(Rsv(t-1)>=C(t)+Tx(t)/s–RMD(t)/s,
RMD(t)/s,If( Rsv(t-1)>0,C(t)+Tx(t)/s–Rsv(t-1),C(t)+Tx(t)/s)))
Moreover, Rsv(t-1) is included with V(t) in the calculation of the limit on C(t) given by C*(t). As a result, the withdrawal given by (1) could at some point exceed V(t). In such an event any funds in the portfolio are used to cover as much of the withdrawal as possible and the remainder is obtained from the reserve. Subsequent s*C(t)+Tx(t) are covered from the reserve.
Taking into account the possibility that V(t) may not be larger than the withdrawal given
by (1), V(t+1) is given by:
If(V(t) >(1),(V(t)–(1))*(1+R(t)),0)
and TxInc(t) by:
If(V(t)>(1),(1),V(t))+10,000
Since V(t+1)=0 when V(t)<=(1) note that RMD(t+1) is also zero in this case. Moreover, at t+1 (1) is also zero because (1) is equal to the RMD when the withdrawal is being funded by the reserve and RMD(t+1)=0. TxInc(t+1) is therefore equal to 10,000 in this case as are subsequent values of taxable income.
RMD(t) adds to the reserve when it exceeds s*C(t)+Tx(t). The reserve is reduced when RMD(t) is less than s*C(t)+Tx(t), and there are funds in the reserve. Assuming V(t)>(1) the change in the reserve at the beginning of t is therefore given by (2):
(2) If(RMD(t)>s*C(t)+Tx(t),RMD(t)–s*C(t)–Tx(t),-If(Rsv(t-1)>=s*C(t)+Tx(t)–RMD(t),
s*C(t)+Tx(t)-RMD(t),If( Rsv(t-1)>0,Rsv(t-1),0)))
If V(t)<=(1), V(t) is deducted from the portfolio and the remainder of the withdrawal at t comes from the reserve. Any further withdrawals in the future come from the reserve. The value of Rsv(t) is therefore given by the following relation:
Rsv(t-1)+If(V(t)>(1),(2),-If(V(t)>0,sC(t)+Tx(t)–sV(t),sC(t)+Tx(t)))
Posted December 2024